The direct and inverse problem for an inclusion within a heat-conducting layered medium

This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously.     

A Gibbs sampling method to determine biomarkers for asthma

PurposeTo identify potential biomarkers and to uncover the mechanisms underlying asthma based on Gibbs sampling.MethodsThe molecular functions (MFs) with genes greater than 5 were determined using AnnotationMFGO of BAGS package, and the obtained MFs were then transformed to Markov chain (MC). Gibbs sampling was conducted to obtain a new MC. Meanwhile, the average probabilities of MFs were computed via MC Monte Carlo (MCMC) algorithm, followed by identification of differentially expressed MFs based on the probabilities of MF more than 0.6. Moreover, the differentially expressed genes (DEGs) and their correlated genes were screened and merged, called as co-expressed genes. Pathways enrichment analysis was implemented for the co-expressed genes.ResultsBased on the gene set more than 5, overall 396 MFs were determined. After Gibbs sampling, 5 differentially expressed MF were acquired according to alfa.pi > 0.6. Moreover, the genes in these 5 differentially expressed MF were merged, and 110 DEGs were identified. Subsequently, 338 co-expressed genes were gained. Based on the P value < 0.01, the co-expressed genes were significantly enriched in 6 pathways. Among these, ubiquitin mediated proteolysis contained the maximum numbers of 35 co-expressed genes, and cell cycle were enriched by the second largest number of 11 co-expressed genes, respectively.ConclusionsThe identified pathways such as ubiquitin mediated proteolysis and cell cycle might play important roles in the development of asthma and may be useful for developing the credible therapeutic approaches for diagnosis and treatment of asthma in future.     

Direct analysis of free amino acids by mixed‐mode chromatography with tandem mass spectrometry

We developed a straightforward, robust, and relatively fast method for the analysis of amino acids by mixed‐mode high‐performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry. The method does not involve derivatization and allows the detection of 21 amino acids, representing a wide range of isoelectric points, in less than 40 min. Chromatographic separation was governed by a silica‐based mixed‐mode column providing simultaneous hydrophobic and ion exchange separation mechanisms. The use of tandem mass spectrometry increased selectivity, reducing potential problems associated with poor selectivity in the chromatographic system. For an injection volume of 1 μL, we obtained detection limits <3 μM for the majority of analytes. For all analytes, a linearity of r > 0.99 was obtained, recovery in matrix was >86%, and the retention times were highly reproducible. The method was successfully applied to soil solution and fungal culture samples, demonstrating the advantages in successfully avoiding issues associated with high amounts of substances that may interfere with derivatization‐based methods. This method represents an alternative to derivatization‐based methods and can be applied in areas where sample matrices are highly complex.     

Absolute Minimal Sampling of Homonuclear 2D NMR TOCSY Spectra for High-Throughput Applications of Complex Mixtures

Modern applications of 2D NMR spectroscopy to diagnostic screening, metabolomics, quality control, and other high-throughput applications are often limited by the time-consuming sampling requirements along the indirect time domain t₁. 2D total correlation spectroscopy (TOCSY) provides unique spin connectivity information for the analysis of a large number of compounds in complex mixtures, but standard methods typically require >100 t₁ increments for an accurate spectral reconstruction, rendering these experiments ineffective for high-throughput applications. For a complex metabolite mixture it is demonstrated that absolute minimal sampling (AMS), based on direct fitting of resonance frequencies and amplitudes in the time domain, yields an accurate spectral reconstruction of TOCSY spectra using as few as 16 t₁ points. This permits the rapid collection of homonuclear 2D NMR experiments at high resolution with measurement times that previously were only the realm of 1D experiments.     

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In Bayesian analysis, the Markov Chain Monte Carlo (MCMC) algorithm is an efficient and simple method to compute posteriors. However, the chain may appear to converge while the posterior is improper, which will leads to incorrect statistical inferences. In this paper, we focus on the necessary and sufficient conditions for which improper hierarchical priors can yield proper posteriors in a multivariate linear model. In addition, we carry out a simulation study to illustrate the theoretical results, in which the Gibbs sampling and Metropolis-Hasting sampling are employed to generate the posteriors.     

Structure dependent sampling in compressed sensing: Theoretical guarantees for tight frames

Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are dependent not only on sparsity but also on the sparsity structure of the underlying signal. This paper extends the result of Adcock, Hansen, Poon and Roman (arXiv:1302.0561, 2013) [2] to the case where the sparsifying system forms a tight frame. By dividing the sampling coefficients into levels, our main result will describe how the amount of subsampling in each level is determined by the local coherences between the sampling and sparsifying operators and the localized level sparsities – the sparsity in each level under the sparsifying operator.     

Role of the Residue Q1919 in Increasing Kinase Activity of G2019S LRRK2 Kinase: A Computational Study

Mutations in multi-domain leucine-rich repeat kinase 2 (LRRK2) have been an interest to researchers as these mutations are associated with Parkinson's disease. G2019S mutation in LRRK2 kinase domain leads to the formation of additional hydrogen bonds by S2019 which results in stabilization of the active state of the kinase, thereby increasing kinase activity. Two additional hydrogen bonds of S2019 are reported separately. Here, a mechanistic picture of the formation of additional hydrogen bonds of S2019 with Q1919 (also with E1920) is presented using ‘active’ Roco4 kinase as a homology model and its relationship with the stabilization of the ‘active’ G2019S LRRK2 kinase. A conformational flipping of residue Q1919 was found which helped to form stable hydrogen bond with S2019 and made ‘active’ state more stable in G2019S LRRK2. Two different states were found within the ‘active’ kinase with respect to the conformational change (flipping) in Q1919. Two doubly-mutated systems, G2019S/Q1919A and G2019S/E1920 K, were studied separately to check the effect of Q1919 and E1920. For both cases, the stable S2 state was not formed, leading to a decrease in kinase activity. These results indicate that both the additional hydrogen bonds of S2019 (with Q1919 and E1920) are necessary to stabilize the active G2019S LRRK2.     

Conformational Effects of Regioisomeric Substitution on the Catalytic Activity of Copper/Calix[8]arene C−S Coupling

Functionalization of the phenolic rim of p-tert-butylcalix[8]arene with phenanthroline to create a cavity leads to formation of two regioisomers. Substitution of positions 1 and 5 produces the known C_2v-symmetric regioisomer 1,5-(2,9-dimethyl-1,10-phenanthroyl)-p-tert-butylcalix[8]arene ( L^1,5 ), while substitution of positions 1 and 4 produces the C_s-symmetric regioisomer 1,4-(2,9-dimethyl-1,10-phenanthroyl)-p-tert-butylcalix[8]arene ( L^1,4 ) described herein. [ Cu(L^1,4)I ] was synthesized from L^1,4 and CuI in good yield and characterized spectroscopically. To evaluate the effect of its cavity on catalysis, Ullmann-type C−S coupling was chosen as proof-of-concept. Selected aryl halides were used, and the results compared with the previously reported Cu(I)/ L^1,5 system. Only highly activated aryl halides generate the C−S coupling product in moderate yields with the Cu(I)/ L^1,4 system. To shed light on these observations, detailed computational investigations were carried out, revealing the influence of the calix[8]arene macrocyclic morphology on the accessible conformations. The L^1,4 regioisomer undergoes a deformation that does not occur with L^1,5 , resulting in an exposed catalytic center, presumably the cause of the low activity of the former system. The 1,4-connectivity was confirmed in the solid-state structure of the byproduct [ Cu(L^1,4 − H) (CH₃CN)₂] that features Cu(I) coordinated inside a cleft defined by the macrocyclic framework.     

催化裂解-金汞齐富集-冷原子吸收光谱仪测定土壤样品中总汞含量

为建立采用催化裂解-金汞齐富集-冷原子吸收光谱仪即直接测汞仪测定土壤样品中汞含量的方法,本研究配制汞总量为0~2 ng、0~15 ng和25~1023 ng的三种不同汞浓度系列的标准工作曲线,选取9个土壤样品,3种国家土壤有证标准物质,同一样品分别进行6组平行测定,并抽取3个土壤样品进行3种不同浓度加标回收试验,以对其方法精密度和准确度进行论证。 结果显示：仪器信号值与Hg总量之间均呈良好的线性关系。根据仪器多次测定空白数据结果,按照称样量0.1 g计算,方法最小检出量为0.09 ng/g;平行测定结果相对标准偏差均小于10%,土壤标准物质测定值与标准物质标准参考值均相符,不同浓度的加标回收率范围为78.4%～92.7%。结果表明催化裂解-金汞齐富集-冷原子吸收光谱仪,可用于批量土壤样品中汞含量的快速测定分析,方法的精密度和准确度可满足测定分析要求,且实验过程中无需前处理消煮,操作方便、快速高效。     

催化光度法时间程序测定土壤中痕量碘

碘是评价环境的重要元素之一,是地球化学勘察样品常测元素。本实验建立了艾斯卡试剂分解-热水提取样品,催化分光光度法时间程序测定碘的方法。详细讨论了艾斯卡试剂手工制作与行星球磨机制作的利弊;;参比液的选择;17℃-25℃不同环境温度条件对实验结果的影响;全程序空白溶液,与36g/L的碳酸钠溶液两种方法制作标准曲线及标准曲线线性范围;样品烧结时间及温度;乙酸用量对样品测试吸光度的影响。结果表明：利用行星球磨机制作艾斯卡试剂,选择试剂空白为参比液,在19℃的恒温环境下,采用36g/L的碳酸钠溶液制作0-8ug/mL标准曲线,样品采用0-300℃、300-500℃、500-750℃三阶段升温,750℃保持30min的烧结程序,乙酸用量为5mL时可以得到可靠的结果。该方法克服了艾斯卡试剂制作困难、样品烧结结块及实验反应速率过快等困难。通过方法学考察表明：基于所建方法碘元素校准曲线系数＞0.999;方法检出限为0.2 mg/kg;测定GSS36、GSS37、GSS38、GSS40、GSS47、GSS48、GSS49等9种国家一级标准物质,结果均在参考值范围内,相对标准偏差RSD＜5%。该方法测定的结果准确度及精密度高、 检出限低、减少碘记忆效应的存在,适用于地球化学勘察土壤样品中碘的测定。